The moment of inertia of any one of the other pennis about the center is given by the parallel axis theorem, , where d is the distance from the new point from the center of mass. for each penny, and thus one has , since the distance from the center of each penny to the center of the configuration is 2r.

Since there are 6 pennies on the outside, one has the total inertia , as in choice (E).

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whats wrong with just doing this:rnrnIp:=I for the 6 penniesrnrnIp=6*(Mr^2)/2rnwe conclude that r=3R because thats how far each disk's boundery is from the center of the systemrn=> Ip= 6 *(3R)^2rn=> Ip= 6*(9) /2rnso Ip=(54/2)MR^2rnrnNow the center penny is just one disk Icp= (1/2)MR^2rnrnTotal I = Ip + Icp = (55/2)MR^2 Choice Ern

physik2011-04-07 16:24:34

Im sorry about the look of this thing.
What I wanted to write was moment of inertia for the 6 disks is
Ip=6*(MR^2)/2

A faster way to do this is to treat the whole configuration as a disk and approximate the moment of intertia:

I=(1/2)(M)(R*R)

M= 7m and R= 3r

This gives I=(56/2)m *r*r which makes sense because this answer should be a little over the actual answer which is now obviously E

f4hy2009-04-02 15:08:03

I wish I thought of that. Thanks.

mr_eggs2009-08-16 21:23:26

but 9*7 is 63...

bcomnes2011-09-22 16:11:53

It is an interesting way to get a ballpark number, but the number you actually get will not make sense if the answer choices include numbers between what this method gets and the actual correct answer.